Point on an Object
We can set a point such that it can be confined on a "path" e.g. a line, an arc, sides of a polygon etc or in a "region" e.g. a sector, a polygon etc. To create such a point, we can use the command Point(path) and PointIn(Region) respectively.
The following is an example about angles in alternate segment. The point Q is restricted on the arc PQR.
Classwork: Create a point on the tangent line and a point in the gray region in the GeoGebra applet below. Then use the Attach / detach tool 
to detach the points.
to detach the points.
You can also construct irregular regions using inequalities and boolean operations.
Classwork: Create a point that is in the region bounded by the parabola and in the GeoGebra applet below.
(Hint: You can use "&&" to obtain the intersection of two regions defined by the inequalities.)